The amount of time that a customer waits on hold at a call center can be modeled by a uniform distribution on the interval from 0 seconds to 120 seconds.

A) Draw a density curve to model the amount of time that a randomly selected customer waits on hold. Be sure to include scales on both axes.
B) About what percent of the time does a customer have to wait between 100 and 120 seconds?

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joaobezerra joaobezerra · Answer 1 · 2021-09-24T13:12:55+02:00

Using the uniform distribution, we have that:

a) The density curve is given at the end of this question.

b) 16.67% of the time does a customer have to wait between 100 and 120 seconds.

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The uniform distribution has two bounds, a and b, and the probability of finding a value between c and d is given by:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

Uniform distribution on the interval of 0 to 120 seconds, thus [tex]a = 0, b = 120[/tex].

The proportion between 100 and 120 seconds is:

[tex]P(100 \leq X \leq 120) = \frac{120 - 100}{120 - 0} = \frac{1}{6} = 0.1667[/tex]

0.1667*100% = 16.67%

16.67% of the time does a customer have to wait between 100 and 120 seconds.

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